Preheat the grill. For the vinaigrette: In a small bowl, combine the tomatoes, shallots, olive oil, parsley and season. Set aside. Heat the oil for frying in a deep saute pan. Begin frying your potatoes when the oil begins to ripple. Carefully turn the potatoes as needed to achieve even browning. Meanwhile, season the lamb medallions, and place them on the grill. Turn after two minutes. Remove the potatoes from the oil, drain and season. Remove the lamb from the grill.
Begin building the mille-feuille: On the plate, put down a potato round, top with a medallion of lamb and a slice of cheese. Repeat, ending with a potato on top. Drizzle the entire plate with the tomato vinaigrette.